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LogarithmsAlgebraHigh schoolabout 0:35

Evaluate log_3(54) - log_3(2): animated lesson

A narrated, step-by-step logarithms video lesson with captions. Final answer: 3.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    log⁡3(54)−log⁡3(2)\log_{3}\left(54\right)-\log_{3}\left(2\right)
  2. 2. Step by step
    1. log⁡3(54)−log⁡3(2)\log_{3}\left(54\right)-\log_{3}\left(2\right)
      Read the expression
    2. log⁡3(54)−log⁡3(2)=3\log_{3}\left(54\right)-\log_{3}\left(2\right) = 3
      Evaluate using the order of operations (parentheses, exponents, multiplication and division, addition and subtraction)
  3. 3. The answer
    33

    log(54, 3) - log(2, 3) = 3

  4. 4. Check
    • Decimal value: 3

Transcript

The problem. Here is the problem: log(54, 3) minus log(2, 3). Evaluate a numerical expression.

Step by step. Read the expression. Evaluate using the order of operations (parentheses, exponents, multiplication and division, addition and subtraction).

The answer. So the answer is 3. Operations are applied in the standard order: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right.

Check. Decimal value: 3.

About logarithms

Evaluate logarithms and solve logarithmic equations using the laws of logs.

Evaluate log_3(54) - log_3(2): Animated Step-by-Step Lesson